Lemma 2.4 (Lemma 2.1, [1]}) 
Let \(X\subset [1, 2]\)  be a \(\delta \) -separated subset and suppose that \(|X|=\delta ^{-\sigma }\)  for some \(0<\sigma <1\) . Suppose that
\(|X+X|_{\delta }\le K|X|.\) 
